The Annals of Statistics

Asymptotic Distribution of an Estimator of the Boundary Parameter of an Unstable Process

M. M. Rao

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Abstract

The limit distribution of the least squares estimator $\hat{\alpha}$ of the parameter $\alpha$ of the first order stochastic difference equation, in the boundary case $|\alpha| = 1$, is presented. With this, the asymptotic distributional problem for any real $\alpha$ in the first order case is completely settled.

Article information

Source
Ann. Statist., Volume 6, Number 1 (1978), 185-190.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344077

Digital Object Identifier
doi:10.1214/aos/1176344077

Mathematical Reviews number (MathSciNet)
MR458676

Zentralblatt MATH identifier
0378.62018

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 60F05: Central limit and other weak theorems

Keywords
Limit distribution boundary parameter estimator unstable process invariance principle

Citation

Rao, M. M. Asymptotic Distribution of an Estimator of the Boundary Parameter of an Unstable Process. Ann. Statist. 6 (1978), no. 1, 185--190. doi:10.1214/aos/1176344077. https://projecteuclid.org/euclid.aos/1176344077


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Corrections

  • See Correction: M. M. Rao. Correction to "Asymptotic Distribution of an Estimator of the Boundary Parameter of an Unstable Process". Ann. Statist., Volume 8, Number 6 (1980), 1403--1403.